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Probability in Banach Spaces IV pp 54–83Cite as

Banach space valued processes with independent increments and stochastic integration

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References

  1. A. ARAUJO, E. GINÉ: The central limit theorem for real and Banach valued random variables. New York-Chichester-Brisbane-Toronto: John Wiley & Sons 1980.

    MATH  Google Scholar 

  2. A. BADRIKIAN: Prolégomènes au calcul des probabilités dans les Banach. In: Ecole d'Eté de Probabilités de Saint-Flour V-1975, Ed. P.L. Hennequin. Lecture Notes in Math. 539. Berlin-Heidelberg-New York: Springer 1976.

    Chapter  Google Scholar 

  3. D.L. BURKHOLDER: Distribution function inequalities for martingales. The Annals of Probability 1, 19–42 (1973).

    Article  MathSciNet  MATH  Google Scholar 

  4. J. DIEUDONNÉ: Foundations of modern analysis. New York-London: Academic Press 1969.

    MATH  Google Scholar 

  5. E. DETTWEILER: Grenzwertsätze für Wahrscheinlichkeitsmaße auf Badrikianschen Räumen. Z. Wahrscheinlichkeitstheorie verw. Gebiete 34, 285–311 (1976).

    Article  MathSciNet  MATH  Google Scholar 

  6. E. DETTWEILER: A characterization of the Banach spaces of type p by Lévy measures. Math. Z. 157, 121–130 (1977).

    Article  MathSciNet  MATH  Google Scholar 

  7. E. DETTWEILER: Poisson measures on Banach lattices. In: Probability measures on groups. Proceedings of the 6th conference in Oberwolfach, Ed. H. Heyer. Lecture Notes in Math. 928, 16–45. Berlin-Heidelberg-New York: Springer 1982.

    Chapter  Google Scholar 

  8. E.B. DYNKIN: Die Grundlagen der Theorie der Markoffschen Prozesse. Berlin-Göttingen-Heidelberg: Springer 1961.

    Book  MATH  Google Scholar 

  9. I.I. GIHMAN, A.V. SKOROHOD: The theory of stochastic processes II. Berlin-Heidelberg-New York: Springer 1975.

    Book  MATH  Google Scholar 

  10. J.B. GRAVERAUX, J. PELLAUMAIL: Formule de Ito pour des processus non continus à valeurs dans des espaces de Banach. Ann. Inst. Henri Poincaré, Section B, Vol. 10, 399–422 (1974).

    MathSciNet  MATH  Google Scholar 

  11. H. HEYER: Probability measures on locally compact groups. Berlin-Heidelberg-New York: Springer 1977.

    Book  MATH  Google Scholar 

  12. J. HOFFMANN-JØRGENSEN, G. PISIER: The law of large numbers and the central limit theorem in Banach spaces. Ann. Prob. 4, 587–599 (1976).

    Article  MathSciNet  MATH  Google Scholar 

  13. J. HOFFMANN-JØRGENSEN: Probability in Banach Spaces. In: Ecole d'Eté de Probabilités de Saint-Flour VI-1976, Ed. P.L. Hennequin. Lecture Notes in Math. 598. Berlin-Heidelberg-New York: Springer 1977.

    Chapter  Google Scholar 

  14. J. LINDENSTRAUSS, L. TZAFRIRI: Classical Banach Spaces II, Function Spaces. Berlin-Heidelberg-New York: Springer 1979.

    Book  MATH  Google Scholar 

  15. B. MAUREY: Probabilités cylindriques, type et ordre, applications radonifiantes. Séminaire Maurey-Schwartz, Ecole Polytechnique, Paris 1972–1973.

    Google Scholar 

  16. M. METIVIER: The stochastic integral with respect to processes with values in a reflexiv Banach space. Theory of Prob. Appl. 19, 758–787 (1974).

    Article  MathSciNet  MATH  Google Scholar 

  17. M. METIVIER, J. PELLAUMAIL: Stochastic Integration. New York-London-Toronto-Sydney-San Francisco: Academic Press 1980.

    MATH  Google Scholar 

  18. G. PISIER: Martingales with values in uniformly convex spaces. Israel J. Math. 20, 326–350 (1975).

    Article  MathSciNet  MATH  Google Scholar 

  19. J. ROSINSKI: Central limit theorems for dependent random vectors in Banach spaces. In: Martingale theory in harmonic analysis and Banach spaces, Proceedings, Cleveland 1981, Eds J.-A. Chao, W.A. Woyczynski. Lecture Notes in Math. 939. Berlin-Heidelberg-New York: Springer 1982.

    Google Scholar 

  20. W.A. WOYCZYNSKI: Geometry and martingales in Banach spaces. In: Winter School on Probability, Karpacz 1975, 229–275. Lecture Notes in Math. 472. Berlin-Heidelberg-New York: Springer 1975.

    Google Scholar 

  21. W.A. WOYCZYNSKI: Geometry and martingales in Banach spaces II. Adv. in Probability, vol 4, 267–517. New York: Decker 1978.

    Google Scholar 

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Authors and Affiliations

  1. Mathematisches Institut der Universität Tübingen, Auf der Morgenstelle 10, 74 Tübingen, Germany

    E. Dettweiler

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  1. E. Dettweiler
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Anatole Beck Konrad Jacobs

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© 1983 Springer-Verlag

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Dettweiler, E. (1983). Banach space valued processes with independent increments and stochastic integration. In: Beck, A., Jacobs, K. (eds) Probability in Banach Spaces IV. Lecture Notes in Mathematics, vol 990. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0064263

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  • DOI: https://doi.org/10.1007/BFb0064263

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-12295-1

  • Online ISBN: 978-3-540-39870-7

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